Category

# Higher Mathematical Computation

216 items

• ### AggregationSystem

Evolve a 2D array of cells by randomly adding new cells at positions with certain neighborhood configurations

• ### AlgebraicSubstitutionTiling

Return a substitution tiling

• ### Antidiagonal

Give the antidiagonal of a matrix

• ### AntidiagonalMatrixQ

Tests whether a matrix is an antidiagonal matrix

• ### ArcsineLawRandomnessTest

Use the arcsine law to assess the randomness of a sequence of zeros and ones

• ### AreaBetweenCurves

Find the area between two plane curves

• ### AxisAngle

Generate the axis-angle representation of a three-dimensional rotation matrix

• ### BacktrackSearch

Solve computational problems using a generic backtracking algorithm

• ### BasisFromVector

Generate an orthonormal basis from a given 3D real vector

• ### BesselSimplify

Simplify Bessel functions in expression

• ### BickleyKi

Evaluate the Bickley function

• ### BinaryCodedTernary

Self-delimiting number representation

• ### BinaryRunRandomnessTest

Conduct a runs–based test on a sequence of zeros and ones

• ### BinomialMod

Efficient computation of a binomial coefficient modulo a given number

• ### BinormalSurface

Compute the binormal surface to a curve

• ### BitBooleanFunction

Apply a Boolean function to corresponding bits in integers

• ### Bjorling

Compute the Björling formula

• ### BoundaryElementMeshJoin

Join multiple boundaries to form a single boundary ElementMesh

• ### ButcherColumnConditions

Give the column-simplifying conditions for Runge–Kutta methods

• ### ButcherPhi

Compute the weight of a Butcher tree

• ### ButcherPrincipalError

Get a list of terms in the Taylor series expansion of the error for Runge–Kutta methods

Give the quadrature conditions for Runge–Kutta methods

• ### ButcherRowConditions

Give the row-simplifying conditions for Runge–Kutta methods

• ### ButcherTreeCount

Get a list of the number of Butcher trees through a given order

• ### ButcherTreeData

Get characteristics of Butcher trees, such as the height, width, order, density and number of labelings

• ### ButcherTreeSimplify

Get the butcher trees through a given order that are not reduced by Butcher’s quadrature or row- or column-simplifying conditions

• ### CanalSurface

Compute the parametrization of a canal surface

• ### CanonicalHypergraph

Find a canonical version of a directed hypergraph

• ### CatacausticCurvePlot

Plot the catacaustic of a curve

• ### CayleyNestGraph

Create a generalized Cayley graph from generators and relations

• ### ChainD

Get the derivative with respect to a function

• ### ChaosGame

Plot iterations for the 2D chaos game

• ### ChebyshevPsi

Calculate the value of the second Chebyshev function ψ(x)

• ### ChebyshevTheta

Calculate the value of the first Chebyshev function θ(x)

• ### ChiSquareRandomnessTest

Test a sequence of zeroes and ones (or a set of random reals between 0 and 1) for equidistribution and return a p-value

• ### ChristoffelSymbol

Return the Christoffel symbol for a given metric

• ### ChromaticNumber

Compute the vertex chromatic number of a graph

• ### ClausenCl

Compute the Clausen functions

• ### Cofactor

Get a cofactor of a matrix

• ### Collatz

Get the Collatz sequence starting with a given value

• ### ColumnSpace

Compute properties of the column space of a matrix

• ### ComplexTransformImage

Add a complex transformation to an image

• ### Composite

Get the nth composite number

• ### ConjugatePartition

Switch the rows and columns of a partition

• ### ConnectedHypergraphQ

Determine whether a hypergraph is connected

• ### Cos2PiOverFermatPrime

Closed form of cos(2π/p) where p is a Fermat prime (3, 5, 17, 257, 65537) a la Gauss

• ### CousinPrimes

Get the pairs of primes that differ by 4

• ### CumulativeAverages

Calculate the cumulative averages of a list

• ### CUSUMMaxRandomnessTest

Conduct a cumulative sum-based randomness test that creates a test statistic from the maximum value that a cumulative sums random walk achieves

• ### CyclicTagSystem

Compute the evolution of a cyclic tag system

• ### DarbouxVector

Compute the Darboux vector field of a curve

• ### DerangementQ

Test whether the permutation list is completely scrambled

• ### Derangements

Give all the ways the numbers 1, 2, …, n can be scrambled completely

• ### DescendingSublists

Split a list at its left-to-right maxima

• ### DiagonalizeMatrix

Get the diagonalized matrix of a given matrix

• ### DyckWords

Give all possible ways to form proper brackets

• ### DynamicCellularAutomaton

Generate a cellular automaton evolution with initial conditions chosen by a click

• ### EgyptianFraction

Compute Egyptian fractions using different methods

• ### EinsteinSummation

Given tensors and their indices, sum over repeated indices

• ### EnneperWeierstrass

Compute the Enneper-Weierstrass parametrization

• ### EnumerateSubstitutionSystemRules

Enumerate possible inequivalent string substitution rules with a given signature

• ### EulerianNumber

Get the number of permutations with a given number of ascents

• ### Excess01Ruler

Find a near-minimal set of integer marks so that all integers up to a given length are represented as differences

• ### ExtendedGroebnerBasis

Compute a Groebner basis and a conversion matrix from the input polynomials to the basis

• ### ExtendedLatticeReduce

Compute a reduced basis for a set of vectors, along with a unimodular matrix that converts from the vectors to the reduced basis

• ### FabiusF

Evaluate the Fabius function

• ### FactorGraph

Get a graph representation for the factorization of an integer

• ### FactorialMod

Fast factorial modulo a given number

• ### FerrersDiagram

Display the Ferrers diagram of a partition with dots

• ### Fibbinary

Get the fibbinary sequence

• ### FibonacciEncode

Fibonacci-digit encoding for a number

• ### FindEquationalModels

Find instances of a binary operator that satisfy equational constraints

• ### FindGroupIsomorphism

Find up to a specified number of isomorphisms between two permutation groups

• ### FindHypergraphIsomorphism

Find all isomorphisms between two orderless (undirected) hypergraphs

• ### FindNestPeriod

Try to find the repetition period for nesting of a function

• ### FindOrderedHypergraphIsomorphism

Find isomorphisms between two ordered (directed) hypergraphs

• ### FindProperColorings

Find all proper k-colorings of a specified graph

• ### FormatFactorization

Express an integer factorization as it would be seen in a factorization table

• ### FractionalDPolynomialRoots

Compute and visualize the roots of fractional (noninteger) derivatives of polynomials

• ### FrobeniusSymbolFromPartition

Get a pair of lists representing the Ferrers diagram of a partition

• ### FromInversionVector

Construct the permutation list corresponding to the given inversion vector

• ### FromTensor

Convert TensorContract expressions into an equivalent form using Dot and Tr

• ### FubiniNumber

Count the number of ways to partition a set where the order of the subsets matters

• ### FunctionJectivity

Determine the injectivity and surjectivity of a function

• ### GaltonBoardModel

Model ball trajectories in a 2D Galton board using Hertzian force laws between the ball and the pegs

• ### GaussianCurvature

Compute the Gaussian curvature of a surface

Find the error in the Gaussian quadrature approximation of a function’s integral

Get a list of abscissa-weight pairs based on the Gaussian quadrature

• ### GeneralizedChaosGame

Create fractals by random partial jumps toward reference points

• ### Goldbach

Get all representations of an even integer as the sum of two primes

• ### GramianReduce

Find a unimodular conversion matrix corresponding to a lattice Gramian matrix

• ### GrayCodeKSubsets

Get k-subsets of a given set in minimum change order

• ### GrayCodeSubsets

Get subsets of a given set in minimum change order

• ### HappyNumberQ

Test whether an integer is a happy number

Get steps of Hofstadter's MU riddle

• ### HookLengths

Get the list of lists whose entries are the hook lengths of the entries of a Young diagram

• ### IndexedOrderedTuple

Give the index of an ordered tuple or return the ordered tuple with that index

• ### IndexedSubset

Give the index of a subset or return the subset with that index

• ### IntegerCompositions

Generate all compositions of an integer into the specified number of parts

• ### IntegerPartitionFrequency

Counts the number of times an integer k appears within all possible ways to partition an integer n without calculating n’s integer partitions

• ### IntegerPartitionQ

Check whether the argument is a weakly decreasing list of positive integers

• ### IntegerSpectralDecomposition

Determine the spectral decomposition of an integer in a modular number system

• ### IntegralApproximationPlot3D

Compute and plot the approximation to the integral of a function of two variables on a rectangle using different methods and partition types

• ### InversionVectorQ

Check if a list is the inversion vector of a permutation written as a list

• ### IrregularPeriodogram

Compute a periodogram for data from unevenly spaced intervals

• ### IsingModelCA

Simulate the Ising model using a cellular automata

• ### IsomorphicHypergraphQ

Determine whether two orderless (undirected) hypergraphs are isomorphic

• ### IsomorphicOrderedHypergraphQ

Determine whether two ordered (directed) hypergraphs are isomorphic

• ### JacobiEpsilon

Evaluate the Jacobi epsilon function

• ### JosephusPermutation

Find the solution of the Josephus problem

• ### KruskalAlgorithm

Find the minimal spanning tree for a given set of points in Euclidean space

• ### KSetPartitions

Give all possible ways to partition a set into a given number of subsets, ignoring order of blocks and within blocks

• ### KullbackLeiblerDivergence

Calculate the Kullback–Leibler divergence between two distributions

• ### LargestPrimeFactor

Find the largest prime factor of a given integer

• ### LargestPrimeGap

Give the greatest gap between the primes up to the argument

• ### Logit

The logit function from probability

• ### LSystemPlot

Display an L-system

• ### LuckyNumbers

Get a list of lucky numbers

• ### MobileAutomaton

Compute the evolution of a mobile automaton

• ### MobileAutomatonPlot

Visualization of the evolution of a mobile automaton

• ### MobileAutomatonRulePlot

Generate the rule icon for a mobile automaton

• ### MockTheta

Implement the Ramanujan mock theta functions

• ### ModularTessellation

Computes polygons, circles, compositions, and transformation functions for the tessellation of the upper half-plane by the modular group.

• ### ModusPonensToEquational

Convert an axiom system from modus ponens to equational form

• ### Monus

Truncate negative numbers in the result of subtraction

• ### MultisetCardinality

Determine the cardinality for a multiset

• ### MultisetComplement

Perform the complement operation on multisets

• ### MultisetDiceDissimilarity

Compute the Dice dissimilarity of two multisets

• ### MultisetInclusionQ

Test whether or not one multiset is included in another multiset

• ### MultisetIntersection

Perform the intersection operation on multisets

• ### MultisetJaccardDissimilarity

Compute the Jaccard dissimilarity of two multisets

• ### MultisetProduct

Perform the product operation on multisets

• ### MultisetSokalSneathDissimilarity

Compute the Sokal–Sneath dissimilarity of two multisets

• ### MultisetSum

Perform the sum operation on multisets

• ### MultisetSupport

Determine the support for a multiset

• ### MultisetSymmetricDifference

Get the symmetric difference of the given lists

• ### MultisetUnion

Perform the union operation on multisets

Numerically evaluate the gradient of a function summed over the eigenvalues of a matrix, with respect to matrix parameters

• ### NewtonCotesError

Find the error in the Newton–Cotes quadrature formula

• ### NewtonCotesWeights

Get the abscissa–weight pairs of the elementary Newton–Cotes formula

• ### NextGrayCodeSubset

Get the successor, in Gray code order, of a given subset

• ### NextIntegerComposition

Get the next composition of an integer in canonical order

• ### NextIntegerPartition

Get the next partition of an integer in reverse lexicographic order

• ### NextKSubset

Get the lexicographic successor of a k-subset of a list

• ### NextLexicographicSubset

Get the next subset of a given set in lexicographic order

• ### NextPermutation

Get the next permutation in lexicographic order

• ### NFAPlot

Plot a nondeterministic finite automaton

• ### NFASimulation

Simulate the behavior of a nondeterministic finite automaton

• ### NInverseLaplaceTransform

Find the numerical approximation for the inverse Laplace transform

• ### NormalSurface

Compute the normal surface of a curve

• ### NthSubset

Get the subset of a list for a given index

• ### Nullity

Compute the nullity of a matrix

• ### OrderedTupleFromIndex

Get the ordered tuple with the given index and length

• ### OrderedTupleIndex

Give the index of an ordered tuple

• ### PartitionCrank

Get Dyson's crank of an integer partition

• ### PartitionFromFrobeniusSymbol

Construct the corresponding partition, given a Frobenius symbol

• ### PartitionRank

The largest part minus the number of parts of a partition

• ### PascalsTriangle

Display a given number of rows in Pascal's triangle

• ### PenroseTile

Make plots of Penrose tiles

• ### PermutationInvolutionQ

Test whether a permutation equals its inverse

• ### PhiNumberSystem

Get a list of powers of the golden ratio which sum to a given integer

• ### PlouffeP

Get the value of the Plouffe P function

• ### PolynomialHermiteDecomposition

Compute the Hermite decomposition of a matrix of univariate polynomials

• ### PolynomialSmithDecomposition

Compute the Smith decomposition of a matrix of univariate polynomials

• ### PopovDecomposition

Compute the Popov decomposition of a matrix of univariate polynomials

• ### PositionsByFirstAppearance

Replace elements with their position of first appearance when flattened

• ### PowerSubdivide

Subdivide an interval such that the ratio of subsequent elements is constant

• ### PowerTowerMod

Give the remainder on division of a power tower expression

• ### PrimeQCertificateCheck

Test if a certificate can be used for ascertaining the primality or compositeness of a number

• ### PrimitiveRootOfUnityList

Get the set of primitive nth roots of unity

• ### ProvablePrimeQ

Certify a number as provably prime

Compute the quadratic residues of an integer

• ### QuantumTensorAutomaton

A quantum cellular automaton model that evolves the tensor product of a collection of initial qubits using arbitrary compositions of unitary operators for a finite number of steps

• ### Quaternion

Represent a quaternion object

• ### RaggedDigitsPlot

Plot an array of digits, allowing them to be ragged on the left

• ### RationalInterpolation

Find a rational interpolation of a function

• ### ReasonableRuler

Find a near minimal set of marks for an integer length ruler so that all smaller integer distances are measurable

• ### RiemannSurfacePlot3D

Plot Riemann surfaces of compositions of elementary functions

• ### RollingCurve

Compute a rolling curve

• ### RowSpace

Compute properties of the row space of a matrix

• ### RunCountRandomnessTest

Conduct a runs up–based randomness test on a sequence of random reals between 0 and 1

• ### RungeKuttaOrderConditions

List equations for Runge–Kutta methods

• ### RunLengthRandomnessTest

Conduct a randomness test on a sequence of random reals between 0 and 1 using run lengths of increasing subsequences

• ### SequentialCellularAutomaton

Cellular automaton evolution with the order of each cell update specified

• ### SequentialSubstitutionSystem

Compute the evolution of a sequential substitution system

• ### SequentialSubstitutionSystemPlot

Visualization of the evolution of a sequential substitution system

• ### SequentialSubstitutionSystemRulePlot

Generate the rule icon for a sequential substitution system

• ### SerialRandomnessTest

Conduct an empirically derived test that assesses randomness using the frequencies of serial combinations of 0s and 1s

• ### SexyPrimes

Get the pairs of primes that differ by 6

• ### SimplexMeasure

Get the measure of a simplex or simplicial complex

• ### SmallestPartsFunction

Total number of smallest parts in the partitions of a positive integer

• ### SmallIntegerLinearSolve

Find a small solution to a system of linear equations over the integers

• ### SpectralRandomnessTest

Use a discrete cosine transform–based method to test the randomness of a sequence of random reals

• ### StandardOrderFromIndex

Get the standard ordering of the desired index

• ### StandardOrderIndex

Get the index of a list of integers in standard order

• ### StandardSimplex

Get the standard simplex for a specified dimension

• ### StemLeafPlot

Construct a stem-and-leaf diagram

• ### StrictIntegerCompositions

Generate the zero-free compositions of a positive integer

• ### SupportSizeEstimate

Estimate the full size of a set given the number of distinct results in a sample

• ### SymbolicSystem

Get the evolution of a symbolic system

• ### TagSystem

Compute the evolution of a tag system

• ### TagSystemRulePlot

Generate the rule icon for a tag system

• ### TangentDevelopableSurface

Compute the tangent developable surface of a curve

• ### TensorCoordinateTransform

Transform components of tensors with arbitrary rank with regard to their transformation behavior under any given mapping

• ### TensorIndexJuggling

Given a metric, convert between covariant and contravariant components of a tensor

• ### ToInversionVector

Get the inversion vector of a permutation written as a list

• ### Totatives

Get the integers from 1 to n that have no common proper factor with n

• ### ToTensor

Convert an expression involving Dot and Tr into an equivalent expression using TensorContract

• ### TupperCipher

Encrypt with Tupper’s self-referential formula

• ### TupperDecipher

Decrypt with Tupper’s self-referential formula

• ### TwinPrimes

Get the pairs of primes that differ by 2

• ### UlamSequence

Starting with the third term, give the least integer expressible uniquely as the sum of two distinct earlier terms

• ### ValidGraphColoring

Check if the given graph coloring is valid

• ### VarianceAround

Calculate the variance of a list along with its uncertainty

• ### WastefulNumberQ

Test whether an integer is a wasteful number

• ### ZeckendorfRepresentation

Give the 0–1 list that indicates the unique nonconsecutive Fibonacci numbers that sum to the non-negative integer input